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Loo’s theorem asserts that the space of all branched minimal      2 2      -spheres of degree      d d       in      S 4 ( 1 ) {S^4}(1)       is connected. The main theorem in this paper is that the assertion is still true for      S 2 m ( 1 ) {S^{2m}}(1)      . It is shown that any branched minimal      2 2      -sphere in      S 2 m ( 1 ) {S^{2m}}(1)       can be deformed, preserving its degree, to a meromorphic function.

Connectedness of the space of minimal 2-spheres in 𝑆^{2𝑚}(1)